Cohomology of $GL_N(\mathbb{Z})$ for $N>7$, trivialilty of $K_8(\mathbb{Z})$ and arithmetical applications
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Speaker:
Philippe Elbaz-Vincent
Affiliation:
Université Grenoble Alpes/HCM
Date:
Tue, 27/03/2018 - 14:00 - 15:00
Location:
MPIM Lecture Hall
Parent event:
Seminar on Algebra, Geometry and Physics Using techniques from lattices and new methods for building the low-dimensional parts of the Voronoi complexes associated to $GL_N(\mathbb{Z})$ for $N>7$, we show how we can get partial informations on the cohomology of $GL_N(\mathbb{Z})$
and use it to prove the triviality of $K_8(\mathbb{Z})$ and deduce some arithmetical consequences. We will also discuss the
algorithmic complexity of the methods involved.
This is based on joint work with M. Dutour-Sikiric, S. Kupers and J. Martinet.
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